On uniqueness and nonuniqueness in the plane creeping flows of second order fluids

R. R. Huilgol

doi:10.1137/0124023

On uniqueness and nonuniqueness in the plane creeping flows of second order fluids

R. R. Huilgol

Research output: Contribution to journal › Article › peer-review

42 Citations (Scopus)

Abstract

The plane creeping flows of a second order incompressible viscoelastic fluid are considered and two theorems are derived to establish when the velocity field of such a fluid is identical to that of an incompressible Newtonian fluid. Application of the first theorem to three flows in unbounded domains is made and it is found that these three flows, respectively, have the same velocity fields as their Newtonian counterparts, and that these velocity fields are uniquely determined. The second theorem is used to show that when it is violated, "non-Newtonian velocity fields" may exist and an example is given, illustrating nonuniqueness in the velocity field.

Original language	English
Pages (from-to)	226-233
Number of pages	8
Journal	SIAM Journal on Applied Mathematics
Volume	24
Issue number	2
DOIs	https://doi.org/10.1137/0124023
Publication status	Published - Mar 1973
Externally published	Yes

Bibliographical note

Funding Information:
Received by the editors March 17, 1972. Department of Mechanics, Illinois Institute of Technology, Chicago, Illinois 60616. This resea"rch was supported in part by the National Science Foundation under Grant GP-32321.

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title = "On uniqueness and nonuniqueness in the plane creeping flows of second order fluids",

abstract = "The plane creeping flows of a second order incompressible viscoelastic fluid are considered and two theorems are derived to establish when the velocity field of such a fluid is identical to that of an incompressible Newtonian fluid. Application of the first theorem to three flows in unbounded domains is made and it is found that these three flows, respectively, have the same velocity fields as their Newtonian counterparts, and that these velocity fields are uniquely determined. The second theorem is used to show that when it is violated, {"}non-Newtonian velocity fields{"} may exist and an example is given, illustrating nonuniqueness in the velocity field.",

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N2 - The plane creeping flows of a second order incompressible viscoelastic fluid are considered and two theorems are derived to establish when the velocity field of such a fluid is identical to that of an incompressible Newtonian fluid. Application of the first theorem to three flows in unbounded domains is made and it is found that these three flows, respectively, have the same velocity fields as their Newtonian counterparts, and that these velocity fields are uniquely determined. The second theorem is used to show that when it is violated, "non-Newtonian velocity fields" may exist and an example is given, illustrating nonuniqueness in the velocity field.

AB - The plane creeping flows of a second order incompressible viscoelastic fluid are considered and two theorems are derived to establish when the velocity field of such a fluid is identical to that of an incompressible Newtonian fluid. Application of the first theorem to three flows in unbounded domains is made and it is found that these three flows, respectively, have the same velocity fields as their Newtonian counterparts, and that these velocity fields are uniquely determined. The second theorem is used to show that when it is violated, "non-Newtonian velocity fields" may exist and an example is given, illustrating nonuniqueness in the velocity field.

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ER -

On uniqueness and nonuniqueness in the plane creeping flows of second order fluids

Abstract

Bibliographical note

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